Understanding Number Systems: The Fundamental Concept in Mathematics

what is the number system ?

1. BY : MAKRAM LAYTH RASHEED SUPERVISOR DR.ZAHRAA TARIK ALALI UNIVERSITY OF MOSUL DEPARTMENT OF MECHATRONICS 2023-2024 Digital Logic Design WHAT IS THE NUMBER SYSTEM?

2. Overview Introduction Types of Number System Application comparison reference 1 2 3 4 5

3. Introduction Number systems are systems in mathematics that are used to express numbers in various forms and are understood by computers. A number is a mathematical value used for counting and measuring objects, and for performing arithmetic calculations. Numbers have various categories like natural numbers, whole numbers, rational and irrational numbers, and so on. Similarly, there are various types of number systems that have different properties, like the binary number system, the octal number system, the decimal number system, and the hexadecimal number system. 01 [1]

4. Types of Number System 02 [2]

5. 1. Decimal The decimal number system or the base 10 number system uses 10 digits ranging from 0 to 9 to represent any number. The first position from the rightmost part of a decimal number is known as one's place or unit's place, then the second position is known as ten's place, and so on. Every decimal number is represented by the power of base 10. For example, the number 1457 is represented as: 03

6. 2. Binary The binary number system or the base 2 number system uses only two digits i.e. 0 and 1 to represent any number. For example, the decimal number 14 is represented as 1110 in the binary number system. We need to keep dividing the decimal number by 2 until the quotient becomes 0 and along with that, we need to remember the remainder. When the remainders obtained in the division are represented in reverse order, a binary number is generated. 04

7. 3. Octal The octal number system or the base 8 number system uses 8 digits ranging from 0 to 7 to represent any number. The octal number is very commonly used the computer systems. Every octal number is represented by the power of base 8. For example, the number 215 is represented as: 05

8. 4. Hexadecimal The hexadecimal number system or the base 16 number system uses 16 digits ranging from 0 to 9 (i.e. 10 digits) and A to F (i.e. 6 digits) to represent any number. Refer to the chart shown below to know the representation of hexadecimal numbers. Hexadecimal 1 2 3 4 5 6 7 8 9 A B C D E F Decimal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 06

9. We can convert a decimal number into a hexadecimal number. We need to keep dividing the decimal number by 16 until the remainder becomes 0 and along with that, we need to remember the remainder. When the remainders obtained in the division are represented in reverse order, the hexadecimal number is generated. 07 6

10. Number System First Application Second Application Binary Storing and transferring data within computers and digital devices. Digital logic operations like electronic gates (AND, OR, NOT). Octal Representing IP addresses in computer networks. Programming industrial control systems. Decimal Daily financial calculations like banking operations and shopping. Representing time, date, and mathematical transactions. Hexadecimal Representing colors in computer graphics design. Programming computers and representing memory addresses. Application 08 [3]

11. System Used Digits Highest Value Usage Decimal 0-9 10^n Everyday life and general computing Binary 0 and 1 2^n Computing and electronics Octal 0-7 8^n Some programming and computing applications Hexadecimal 0-9 and A-F 16^n Programming and dealing with addresses/data comparison 09

12. reference 10 https://www.cuemath.com/numbers/number-systems/ https://www.scaler.com/topics/number-system/ https://unacademy.com/content/cat/study-material/mathematics/number-systems-in-real-life-situations/ [1] [2] [3]

13. Thank You